X - y = -2 4x - y = 4

Question

asked Mar 14, 2022 40.3k views

1 Answer

Mitch Schwartz · Answer 1 · 2022-03-18T23:53:08+0000

$\begin{cases} x - y = - 2 \\ 4x - y = 4 \end{cases}$

Use the elimination method as it is faster. We have to eliminate the y-term. (You can eliminate the x-term but it takes longer than eliminating y-term.)

Simply multiply the negative one in one of the equations.

$\begin{cases} - x + y = 2 \\ 4x - y = 4 \end{cases}$

We can finally eliminate the y-term by adding both equations.

$( - x + 4x) + (y - y) = 2 + 4 \\ 3x + 0 = 6 \\ 3x = 6 \\ x = ( 6 )/(3) \longrightarrow \frac{ \cancel{6}}{ \cancel{3}} = 2 \\ x = 2$

Substitute the value of x in any given equations. I will substitute in the first equation.

$x - y = - 2 \\ 2 - y = - 2 \\ 2 + 2 = y \\ 4 = y$

First Equation

$x - y = - 2 \\ 2 - 4 = - 2 \\ - 2 = - 2 \longrightarrow \sf{true} \: \: \green{ \checkmark}$

Second Equation

$4x - y = 4 \\ 4(2) - 4 = 4 \\ 8 - 4 = 4 \\ 4 = 4 \longrightarrow \sf{true} \: \: \green{ \checkmark}$

Hence, the solution is (2,4).

$\begin{cases} x = 2 \\ y = 4 \end{cases}$

Coordinate Form

(2,4)